Gibson or maybe Jepsen. John and Anne from - Kobenhavn [Copenhagen]

circa 1880, John and Anne Gibson (nee Petersen) were exiled from Denmark. He was a military officer who was caught duelling. Apparently went with his family to the USA entering at New Port, living in Minnesota, Illinois and possible Seattle Washington. His son was an infant at this time and he later immigrated to New Zealand. This child was John Gibson and he is my Grandfather. John's siblings included: Seth (also in Dansk military); Jennifer; Fredericka. I simply cannot trace these people - maybe they changed their names and "Gibson" is not the original name?? Can you please help?